Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 90.4% → 96.8%

Time: 16.8s

Alternatives: 18

Speedup: 0.5×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, c \cdot \left(i \cdot \left(-\mathsf{fma}\left(b, c, a\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i))))
     (* 2.0 (fma y x (* c (* i (- (fma b c a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * fma(y, x, (c * (i * -fma(b, c, a))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * fma(y, x, Float64(c * Float64(i * Float64(-fma(b, c, a))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x + N[(c * N[(i * (-N[(b * c + a), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   1. Initial program 94.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 98.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 98.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 38.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 38.5%

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + \left(-c\right) \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

      2. fma-def 69.2%

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, \left(-c\right) \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

      3. *-commutative 69.2%

         \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \left(-c\right) \cdot \color{blue}{\left(\left(c \cdot b + a\right) \cdot i\right)}\right) \]

      4. *-commutative 69.2%

         \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \left(-c\right) \cdot \left(\left(\color{blue}{b \cdot c} + a\right) \cdot i\right)\right) \]

      5. fma-def 69.2%

         \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \left(-c\right) \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   4. Applied egg-rr 69.2%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, c \cdot \left(i \cdot \left(-\mathsf{fma}\left(b, c, a\right)\right)\right)\right)\\ \end{array} \]

Alternative 2: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i))))
     (* 2.0 (* c (* c (* b (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (c * (c * (b * -i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(b * Float64(-i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(c * N[(b * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   1. Initial program 94.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 98.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 98.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 15.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 15.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 61.6%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 61.6%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 61.6%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*l* 61.6%

         \[\leadsto 2 \cdot \left(-\color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      5. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot c\right)}\right) \]

      6. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-c \cdot \left(\color{blue}{\left(i \cdot b\right)} \cdot c\right)\right) \]

      7. associate-*r* 61.5%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(i \cdot \left(b \cdot c\right)\right)}\right) \]

      8. distribute-rgt-neg-in 61.5%

         \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(-i \cdot \left(b \cdot c\right)\right)\right)} \]

      9. associate-*r* 61.6%

         \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{\left(i \cdot b\right) \cdot c}\right)\right) \]

      10. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{\left(b \cdot i\right)} \cdot c\right)\right) \]

      11. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{c \cdot \left(b \cdot i\right)}\right)\right) \]

      12. distribute-rgt-neg-in 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \color{blue}{\left(c \cdot \left(-b \cdot i\right)\right)}\right) \]

      13. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(c \cdot \left(-\color{blue}{i \cdot b}\right)\right)\right) \]

      14. distribute-rgt-neg-in 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right)\right) \]

   8. Simplified 61.6%

      \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(c \cdot \left(i \cdot \left(-b\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* x y) (* c (* t_1 i))))
     (if (<= t_2 5e+296)
       (* (- (+ (* x y) (* z t)) t_2) 2.0)
       (* 2.0 (* c (* t_1 (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+296) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+296) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	elif t_2 <= 5e+296:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	else:
		tmp = 2.0 * (c * (t_1 * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	elseif (t_2 <= 5e+296)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	elseif (t_2 <= 5e+296)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	else
		tmp = 2.0 * (c * (t_1 * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+296], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0

   1. Initial program 71.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 83.4%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000001e296

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   if 5.0000000000000001e296 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 91.6%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 4: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t_2 - \left(c \cdot t_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t_2 - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* c (* c (* b (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (c * (c * (b * -i)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (c * (c * (b * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (t_2 - ((c * t_1) * i)) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * (c * (c * (b * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(b * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * (c * (c * (b * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(c * N[(b * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   1. Initial program 94.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 98.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 98.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 98.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 98.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 98.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 15.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 15.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 15.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 61.6%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 61.6%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 61.6%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*l* 61.6%

         \[\leadsto 2 \cdot \left(-\color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      5. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot c\right)}\right) \]

      6. *-commutative 61.6%

         \[\leadsto 2 \cdot \left(-c \cdot \left(\color{blue}{\left(i \cdot b\right)} \cdot c\right)\right) \]

      7. associate-*r* 61.5%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(i \cdot \left(b \cdot c\right)\right)}\right) \]

      8. distribute-rgt-neg-in 61.5%

         \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(-i \cdot \left(b \cdot c\right)\right)\right)} \]

      9. associate-*r* 61.6%

         \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{\left(i \cdot b\right) \cdot c}\right)\right) \]

      10. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{\left(b \cdot i\right)} \cdot c\right)\right) \]

      11. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{c \cdot \left(b \cdot i\right)}\right)\right) \]

      12. distribute-rgt-neg-in 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \color{blue}{\left(c \cdot \left(-b \cdot i\right)\right)}\right) \]

      13. *-commutative 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(c \cdot \left(-\color{blue}{i \cdot b}\right)\right)\right) \]

      14. distribute-rgt-neg-in 61.6%

          \[\leadsto 2 \cdot \left(c \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right)\right) \]

   8. Simplified 61.6%

      \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(c \cdot \left(i \cdot \left(-b\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ t_3 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* a i)))
        (t_2 (* 2.0 (- (* x y) t_1)))
        (t_3 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.1e+82)
     t_3
     (if (<= c -2.2e+14)
       (* 2.0 (- (* z t) (* i (* a c))))
       (if (<= c -1.1e-36)
         t_2
         (if (<= c 6.5e-7)
           (* 2.0 (+ (* x y) (* z t)))
           (if (<= c 6.6e+38)
             t_2
             (if (<= c 8e+74) (* 2.0 (- (* z t) t_1)) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.1e+82) {
		tmp = t_3;
	} else if (c <= -2.2e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.1e-36) {
		tmp = t_2;
	} else if (c <= 6.5e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.6e+38) {
		tmp = t_2;
	} else if (c <= 8e+74) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (a * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    t_3 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.1d+82)) then
        tmp = t_3
    else if (c <= (-2.2d+14)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= (-1.1d-36)) then
        tmp = t_2
    else if (c <= 6.5d-7) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 6.6d+38) then
        tmp = t_2
    else if (c <= 8d+74) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.1e+82) {
		tmp = t_3;
	} else if (c <= -2.2e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.1e-36) {
		tmp = t_2;
	} else if (c <= 6.5e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.6e+38) {
		tmp = t_2;
	} else if (c <= 8e+74) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (a * i)
	t_2 = 2.0 * ((x * y) - t_1)
	t_3 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.1e+82:
		tmp = t_3
	elif c <= -2.2e+14:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= -1.1e-36:
		tmp = t_2
	elif c <= 6.5e-7:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 6.6e+38:
		tmp = t_2
	elif c <= 8e+74:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(a * i))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	t_3 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.1e+82)
		tmp = t_3;
	elseif (c <= -2.2e+14)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= -1.1e-36)
		tmp = t_2;
	elseif (c <= 6.5e-7)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 6.6e+38)
		tmp = t_2;
	elseif (c <= 8e+74)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (a * i);
	t_2 = 2.0 * ((x * y) - t_1);
	t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.1e+82)
		tmp = t_3;
	elseif (c <= -2.2e+14)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= -1.1e-36)
		tmp = t_2;
	elseif (c <= 6.5e-7)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 6.6e+38)
		tmp = t_2;
	elseif (c <= 8e+74)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e+82], t$95$3, If[LessEqual[c, -2.2e+14], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.1e-36], t$95$2, If[LessEqual[c, 6.5e-7], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e+38], t$95$2, If[LessEqual[c, 8e+74], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.1000000000000001e82 or 7.99999999999999961e74 < c

   1. Initial program 75.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 86.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]

   if -1.1000000000000001e82 < c < -2.2e14

   1. Initial program 88.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

      2. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(i \cdot a\right) \cdot c}\right) \]

      3. associate-*r* 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{i \cdot \left(a \cdot c\right)}\right) \]

      4. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - i \cdot \color{blue}{\left(c \cdot a\right)}\right) \]

   9. Simplified 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - i \cdot \left(c \cdot a\right)\right)} \]

   if -2.2e14 < c < -1.1e-36 or 6.50000000000000024e-7 < c < 6.5999999999999998e38

   1. Initial program 99.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 97.8%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   3. Taylor expanded in c around 0 80.6%

      \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(a \cdot i\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

   5. Simplified 80.6%

      \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

   if -1.1e-36 < c < 6.50000000000000024e-7

   1. Initial program 98.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 76.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 6.5999999999999998e38 < c < 7.99999999999999961e74

   1. Initial program 100.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 6: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* a (* c i))))))
   (if (<= c -7e+83)
     (* (* b (* c (* c i))) -2.0)
     (if (<= c -8.8e+14)
       (* 2.0 (- (* z t) (* i (* a c))))
       (if (<= c -1.05e-40)
         t_1
         (if (<= c 5e-7)
           (* 2.0 (+ (* x y) (* z t)))
           (if (<= c 1.1e+39)
             t_1
             (if (<= c 5.5e+74)
               (* 2.0 (- (* z t) (* c (* a i))))
               (* -2.0 (* (* c i) (* b c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if (c <= -7e+83) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= -8.8e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.05e-40) {
		tmp = t_1;
	} else if (c <= 5e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.1e+39) {
		tmp = t_1;
	} else if (c <= 5.5e+74) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (a * (c * i)))
    if (c <= (-7d+83)) then
        tmp = (b * (c * (c * i))) * (-2.0d0)
    else if (c <= (-8.8d+14)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= (-1.05d-40)) then
        tmp = t_1
    else if (c <= 5d-7) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 1.1d+39) then
        tmp = t_1
    else if (c <= 5.5d+74) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else
        tmp = (-2.0d0) * ((c * i) * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if (c <= -7e+83) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= -8.8e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.05e-40) {
		tmp = t_1;
	} else if (c <= 5e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.1e+39) {
		tmp = t_1;
	} else if (c <= 5.5e+74) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (a * (c * i)))
	tmp = 0
	if c <= -7e+83:
		tmp = (b * (c * (c * i))) * -2.0
	elif c <= -8.8e+14:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= -1.05e-40:
		tmp = t_1
	elif c <= 5e-7:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 1.1e+39:
		tmp = t_1
	elif c <= 5.5e+74:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	else:
		tmp = -2.0 * ((c * i) * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))))
	tmp = 0.0
	if (c <= -7e+83)
		tmp = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0);
	elseif (c <= -8.8e+14)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= -1.05e-40)
		tmp = t_1;
	elseif (c <= 5e-7)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 1.1e+39)
		tmp = t_1;
	elseif (c <= 5.5e+74)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * i) * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (a * (c * i)));
	tmp = 0.0;
	if (c <= -7e+83)
		tmp = (b * (c * (c * i))) * -2.0;
	elseif (c <= -8.8e+14)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= -1.05e-40)
		tmp = t_1;
	elseif (c <= 5e-7)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 1.1e+39)
		tmp = t_1;
	elseif (c <= 5.5e+74)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	else
		tmp = -2.0 * ((c * i) * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+83], N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[c, -8.8e+14], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e-40], t$95$1, If[LessEqual[c, 5e-7], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+39], t$95$1, If[LessEqual[c, 5.5e+74], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.99999999999999954e83

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 87.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 87.2%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 74.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 74.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 74.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 74.8%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 74.8%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 74.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 74.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 76.7%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 76.7%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]

   12. Taylor expanded in c around 0 76.7%

       \[\leadsto \left(\color{blue}{\left({c}^{2} \cdot i\right)} \cdot b\right) \cdot -2 \]
   13. Step-by-step derivation

       1. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

       2. associate-*r* 78.7%

          \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   14. Simplified 78.7%

       \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   if -6.99999999999999954e83 < c < -8.8e14

   1. Initial program 88.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

      2. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(i \cdot a\right) \cdot c}\right) \]

      3. associate-*r* 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{i \cdot \left(a \cdot c\right)}\right) \]

      4. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - i \cdot \color{blue}{\left(c \cdot a\right)}\right) \]

   9. Simplified 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - i \cdot \left(c \cdot a\right)\right)} \]

   if -8.8e14 < c < -1.05000000000000009e-40 or 4.99999999999999977e-7 < c < 1.1000000000000001e39

   1. Initial program 99.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 99.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 82.6%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in z around 0 80.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(a \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 80.5%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot a\right) \cdot i}\right) \]

      2. *-commutative 80.5%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]

      3. associate-*r* 80.5%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{a \cdot \left(c \cdot i\right)}\right) \]

   9. Simplified 80.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - a \cdot \left(c \cdot i\right)\right)} \]

   if -1.05000000000000009e-40 < c < 4.99999999999999977e-7

   1. Initial program 98.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 76.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 1.1000000000000001e39 < c < 5.5000000000000003e74

   1. Initial program 100.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]

   if 5.5000000000000003e74 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 63.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 63.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 63.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 66.1%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 66.1%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 63.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 63.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 68.1%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 68.1%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 68.1%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   12. Step-by-step derivation

       1. expm1-log1p-u 33.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)\right)} \cdot -2 \]

       2. expm1-udef 33.6%

          \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)} - 1\right)} \cdot -2 \]

       3. *-commutative 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{b \cdot \left(\left(c \cdot c\right) \cdot i\right)}\right)} - 1\right) \cdot -2 \]

       4. associate-*l* 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(b \cdot \color{blue}{\left(c \cdot \left(c \cdot i\right)\right)}\right)} - 1\right) \cdot -2 \]

       5. associate-*r* 35.3%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot \left(c \cdot i\right)}\right)} - 1\right) \cdot -2 \]

   13. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} - 1\right)} \cdot -2 \]
   14. Step-by-step derivation

       1. expm1-def 35.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)} \cdot -2 \]

       2. expm1-log1p 71.8%

          \[\leadsto \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \cdot -2 \]

       3. *-commutative 71.8%

          \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)} \cdot -2 \]

       4. *-commutative 71.8%

          \[\leadsto \left(\left(c \cdot i\right) \cdot \color{blue}{\left(c \cdot b\right)}\right) \cdot -2 \]

   15. Simplified 71.8%

       \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)} \cdot -2 \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \]

Alternative 7: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* a i))) (t_2 (* 2.0 (- (* x y) t_1))))
   (if (<= c -1.7e+83)
     (* (* b (* c (* c i))) -2.0)
     (if (<= c -6e+14)
       (* 2.0 (- (* z t) (* i (* a c))))
       (if (<= c -6.2e-37)
         t_2
         (if (<= c 7.2e-7)
           (* 2.0 (+ (* x y) (* z t)))
           (if (<= c 3.5e+48)
             t_2
             (if (<= c 9e+75)
               (* 2.0 (- (* z t) t_1))
               (* -2.0 (* (* c i) (* b c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -1.7e+83) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= -6e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -6.2e-37) {
		tmp = t_2;
	} else if (c <= 7.2e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 3.5e+48) {
		tmp = t_2;
	} else if (c <= 9e+75) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (a * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    if (c <= (-1.7d+83)) then
        tmp = (b * (c * (c * i))) * (-2.0d0)
    else if (c <= (-6d+14)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= (-6.2d-37)) then
        tmp = t_2
    else if (c <= 7.2d-7) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 3.5d+48) then
        tmp = t_2
    else if (c <= 9d+75) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = (-2.0d0) * ((c * i) * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -1.7e+83) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= -6e+14) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -6.2e-37) {
		tmp = t_2;
	} else if (c <= 7.2e-7) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 3.5e+48) {
		tmp = t_2;
	} else if (c <= 9e+75) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (a * i)
	t_2 = 2.0 * ((x * y) - t_1)
	tmp = 0
	if c <= -1.7e+83:
		tmp = (b * (c * (c * i))) * -2.0
	elif c <= -6e+14:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= -6.2e-37:
		tmp = t_2
	elif c <= 7.2e-7:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 3.5e+48:
		tmp = t_2
	elif c <= 9e+75:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = -2.0 * ((c * i) * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(a * i))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	tmp = 0.0
	if (c <= -1.7e+83)
		tmp = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0);
	elseif (c <= -6e+14)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= -6.2e-37)
		tmp = t_2;
	elseif (c <= 7.2e-7)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 3.5e+48)
		tmp = t_2;
	elseif (c <= 9e+75)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * i) * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (a * i);
	t_2 = 2.0 * ((x * y) - t_1);
	tmp = 0.0;
	if (c <= -1.7e+83)
		tmp = (b * (c * (c * i))) * -2.0;
	elseif (c <= -6e+14)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= -6.2e-37)
		tmp = t_2;
	elseif (c <= 7.2e-7)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 3.5e+48)
		tmp = t_2;
	elseif (c <= 9e+75)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = -2.0 * ((c * i) * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.7e+83], N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[c, -6e+14], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.2e-37], t$95$2, If[LessEqual[c, 7.2e-7], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+48], t$95$2, If[LessEqual[c, 9e+75], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.6999999999999999e83

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 87.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 87.2%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 74.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 74.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 74.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 74.8%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 74.8%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 74.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 74.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 76.7%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 76.7%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]

   12. Taylor expanded in c around 0 76.7%

       \[\leadsto \left(\color{blue}{\left({c}^{2} \cdot i\right)} \cdot b\right) \cdot -2 \]
   13. Step-by-step derivation

       1. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

       2. associate-*r* 78.7%

          \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   14. Simplified 78.7%

       \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   if -1.6999999999999999e83 < c < -6e14

   1. Initial program 88.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

      2. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(i \cdot a\right) \cdot c}\right) \]

      3. associate-*r* 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{i \cdot \left(a \cdot c\right)}\right) \]

      4. *-commutative 81.7%

         \[\leadsto 2 \cdot \left(t \cdot z - i \cdot \color{blue}{\left(c \cdot a\right)}\right) \]

   9. Simplified 81.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - i \cdot \left(c \cdot a\right)\right)} \]

   if -6e14 < c < -6.19999999999999987e-37 or 7.19999999999999989e-7 < c < 3.4999999999999997e48

   1. Initial program 99.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 97.8%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   3. Taylor expanded in c around 0 80.6%

      \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(a \cdot i\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

   5. Simplified 80.6%

      \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(i \cdot a\right)}\right) \]

   if -6.19999999999999987e-37 < c < 7.19999999999999989e-7

   1. Initial program 98.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 76.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 3.4999999999999997e48 < c < 9.0000000000000007e75

   1. Initial program 100.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 100.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in x around 0 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(a \cdot i\right)\right)} \]

   if 9.0000000000000007e75 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 63.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 63.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 63.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 66.1%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 66.1%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 63.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 63.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 68.1%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 68.1%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 68.1%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   12. Step-by-step derivation

       1. expm1-log1p-u 33.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)\right)} \cdot -2 \]

       2. expm1-udef 33.6%

          \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)} - 1\right)} \cdot -2 \]

       3. *-commutative 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{b \cdot \left(\left(c \cdot c\right) \cdot i\right)}\right)} - 1\right) \cdot -2 \]

       4. associate-*l* 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(b \cdot \color{blue}{\left(c \cdot \left(c \cdot i\right)\right)}\right)} - 1\right) \cdot -2 \]

       5. associate-*r* 35.3%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot \left(c \cdot i\right)}\right)} - 1\right) \cdot -2 \]

   13. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} - 1\right)} \cdot -2 \]
   14. Step-by-step derivation

       1. expm1-def 35.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)} \cdot -2 \]

       2. expm1-log1p 71.8%

          \[\leadsto \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \cdot -2 \]

       3. *-commutative 71.8%

          \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)} \cdot -2 \]

       4. *-commutative 71.8%

          \[\leadsto \left(\left(c \cdot i\right) \cdot \color{blue}{\left(c \cdot b\right)}\right) \cdot -2 \]

   15. Simplified 71.8%

       \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)} \cdot -2 \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \]

Alternative 8: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1050000 \lor \neg \left(t \leq 2.45 \cdot 10^{+126}\right) \land \left(t \leq 2.85 \cdot 10^{+169} \lor \neg \left(t \leq 2.45 \cdot 10^{+245}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -1050000.0)
         (and (not (<= t 2.45e+126))
              (or (<= t 2.85e+169) (not (<= t 2.45e+245)))))
   (* 2.0 (+ (* x y) (* z t)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -1050000.0) || (!(t <= 2.45e+126) && ((t <= 2.85e+169) || !(t <= 2.45e+245)))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-1050000.0d0)) .or. (.not. (t <= 2.45d+126)) .and. (t <= 2.85d+169) .or. (.not. (t <= 2.45d+245))) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -1050000.0) || (!(t <= 2.45e+126) && ((t <= 2.85e+169) || !(t <= 2.45e+245)))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -1050000.0) or (not (t <= 2.45e+126) and ((t <= 2.85e+169) or not (t <= 2.45e+245))):
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -1050000.0) || (!(t <= 2.45e+126) && ((t <= 2.85e+169) || !(t <= 2.45e+245))))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -1050000.0) || (~((t <= 2.45e+126)) && ((t <= 2.85e+169) || ~((t <= 2.45e+245)))))
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -1050000.0], And[N[Not[LessEqual[t, 2.45e+126]], $MachinePrecision], Or[LessEqual[t, 2.85e+169], N[Not[LessEqual[t, 2.45e+245]], $MachinePrecision]]]], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e6 or 2.45e126 < t < 2.8500000000000001e169 or 2.45000000000000024e245 < t

   1. Initial program 88.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 72.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if -1.05e6 < t < 2.45e126 or 2.8500000000000001e169 < t < 2.45000000000000024e245

   1. Initial program 90.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 83.2%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1050000 \lor \neg \left(t \leq 2.45 \cdot 10^{+126}\right) \land \left(t \leq 2.85 \cdot 10^{+169} \lor \neg \left(t \leq 2.45 \cdot 10^{+245}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -9 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -9e+82)
     (* 2.0 (- (* x y) (* c (* t_1 i))))
     (if (<= c 1.28e+76)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (* c (* t_1 (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= -9e+82) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (c <= 1.28e+76) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (b * c)
    if (c <= (-9d+82)) then
        tmp = 2.0d0 * ((x * y) - (c * (t_1 * i)))
    else if (c <= 1.28d+76) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * (c * (t_1 * -i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= -9e+82) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (c <= 1.28e+76) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= -9e+82:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	elif c <= 1.28e+76:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * (c * (t_1 * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (c <= -9e+82)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	elseif (c <= 1.28e+76)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	tmp = 0.0;
	if (c <= -9e+82)
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	elseif (c <= 1.28e+76)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * (c * (t_1 * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9e+82], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.28e+76], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.9999999999999993e82

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 87.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -8.9999999999999993e82 < c < 1.27999999999999994e76

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 93.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   if 1.27999999999999994e76 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 86.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 10: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -2.1e+83)
     (* 2.0 (- (* x y) (* c (* t_1 i))))
     (if (<= c 2.2e+75)
       (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
       (* 2.0 (* c (* t_1 (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= -2.1e+83) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (c <= 2.2e+75) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (b * c)
    if (c <= (-2.1d+83)) then
        tmp = 2.0d0 * ((x * y) - (c * (t_1 * i)))
    else if (c <= 2.2d+75) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * (c * (t_1 * -i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= -2.1e+83) {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	} else if (c <= 2.2e+75) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= -2.1e+83:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	elif c <= 2.2e+75:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * (c * (t_1 * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (c <= -2.1e+83)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	elseif (c <= 2.2e+75)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	tmp = 0.0;
	if (c <= -2.1e+83)
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	elseif (c <= 2.2e+75)
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * (c * (t_1 * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.1e+83], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+75], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.10000000000000002e83

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 87.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -2.10000000000000002e83 < c < 2.20000000000000012e75

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 98.1%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 98.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 98.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 98.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 98.1%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 93.4%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{a} \cdot \left(c \cdot i\right)\right) \]

   if 2.20000000000000012e75 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 86.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 11: 34.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+221}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (* c i) (- a))))
        (t_2 (* 2.0 (* x y)))
        (t_3 (* 2.0 (* z t))))
   (if (<= y -1.06e-86)
     t_2
     (if (<= y -3.85e-274)
       t_1
       (if (<= y 1.7e-247)
         t_3
         (if (<= y 7.8e+44) t_1 (if (<= y 6.2e+221) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((c * i) * -a);
	double t_2 = 2.0 * (x * y);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (y <= -1.06e-86) {
		tmp = t_2;
	} else if (y <= -3.85e-274) {
		tmp = t_1;
	} else if (y <= 1.7e-247) {
		tmp = t_3;
	} else if (y <= 7.8e+44) {
		tmp = t_1;
	} else if (y <= 6.2e+221) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((c * i) * -a)
    t_2 = 2.0d0 * (x * y)
    t_3 = 2.0d0 * (z * t)
    if (y <= (-1.06d-86)) then
        tmp = t_2
    else if (y <= (-3.85d-274)) then
        tmp = t_1
    else if (y <= 1.7d-247) then
        tmp = t_3
    else if (y <= 7.8d+44) then
        tmp = t_1
    else if (y <= 6.2d+221) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((c * i) * -a);
	double t_2 = 2.0 * (x * y);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (y <= -1.06e-86) {
		tmp = t_2;
	} else if (y <= -3.85e-274) {
		tmp = t_1;
	} else if (y <= 1.7e-247) {
		tmp = t_3;
	} else if (y <= 7.8e+44) {
		tmp = t_1;
	} else if (y <= 6.2e+221) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((c * i) * -a)
	t_2 = 2.0 * (x * y)
	t_3 = 2.0 * (z * t)
	tmp = 0
	if y <= -1.06e-86:
		tmp = t_2
	elif y <= -3.85e-274:
		tmp = t_1
	elif y <= 1.7e-247:
		tmp = t_3
	elif y <= 7.8e+44:
		tmp = t_1
	elif y <= 6.2e+221:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)))
	t_2 = Float64(2.0 * Float64(x * y))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (y <= -1.06e-86)
		tmp = t_2;
	elseif (y <= -3.85e-274)
		tmp = t_1;
	elseif (y <= 1.7e-247)
		tmp = t_3;
	elseif (y <= 7.8e+44)
		tmp = t_1;
	elseif (y <= 6.2e+221)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((c * i) * -a);
	t_2 = 2.0 * (x * y);
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (y <= -1.06e-86)
		tmp = t_2;
	elseif (y <= -3.85e-274)
		tmp = t_1;
	elseif (y <= 1.7e-247)
		tmp = t_3;
	elseif (y <= 7.8e+44)
		tmp = t_1;
	elseif (y <= 6.2e+221)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e-86], t$95$2, If[LessEqual[y, -3.85e-274], t$95$1, If[LessEqual[y, 1.7e-247], t$95$3, If[LessEqual[y, 7.8e+44], t$95$1, If[LessEqual[y, 6.2e+221], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05999999999999997e-86 or 6.20000000000000013e221 < y

   1. Initial program 89.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 55.8%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -1.05999999999999997e-86 < y < -3.84999999999999985e-274 or 1.7000000000000001e-247 < y < 7.8000000000000005e44

   1. Initial program 88.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 94.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 94.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 94.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 94.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 94.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 41.4%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto 2 \cdot \color{blue}{\left(-c \cdot \left(i \cdot a\right)\right)} \]

      2. associate-*r* 48.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot i\right) \cdot a}\right) \]

      3. distribute-lft-neg-in 48.2%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-c \cdot i\right) \cdot a\right)} \]

      4. distribute-rgt-neg-in 48.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot \left(-i\right)\right)} \cdot a\right) \]

   8. Simplified 48.2%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot \left(-i\right)\right) \cdot a\right)} \]

   if -3.84999999999999985e-274 < y < 1.7000000000000001e-247 or 7.8000000000000005e44 < y < 6.20000000000000013e221

   1. Initial program 92.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 37.4%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-274}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+221}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 34.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+221}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -4.5e-112)
     t_2
     (if (<= y 4.4e-247)
       t_1
       (if (<= y 4.5e+45)
         (* 2.0 (* c (* a (- i))))
         (if (<= y 6.2e+221) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -4.5e-112) {
		tmp = t_2;
	} else if (y <= 4.4e-247) {
		tmp = t_1;
	} else if (y <= 4.5e+45) {
		tmp = 2.0 * (c * (a * -i));
	} else if (y <= 6.2e+221) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-4.5d-112)) then
        tmp = t_2
    else if (y <= 4.4d-247) then
        tmp = t_1
    else if (y <= 4.5d+45) then
        tmp = 2.0d0 * (c * (a * -i))
    else if (y <= 6.2d+221) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -4.5e-112) {
		tmp = t_2;
	} else if (y <= 4.4e-247) {
		tmp = t_1;
	} else if (y <= 4.5e+45) {
		tmp = 2.0 * (c * (a * -i));
	} else if (y <= 6.2e+221) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if y <= -4.5e-112:
		tmp = t_2
	elif y <= 4.4e-247:
		tmp = t_1
	elif y <= 4.5e+45:
		tmp = 2.0 * (c * (a * -i))
	elif y <= 6.2e+221:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -4.5e-112)
		tmp = t_2;
	elseif (y <= 4.4e-247)
		tmp = t_1;
	elseif (y <= 4.5e+45)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	elseif (y <= 6.2e+221)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -4.5e-112)
		tmp = t_2;
	elseif (y <= 4.4e-247)
		tmp = t_1;
	elseif (y <= 4.5e+45)
		tmp = 2.0 * (c * (a * -i));
	elseif (y <= 6.2e+221)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-112], t$95$2, If[LessEqual[y, 4.4e-247], t$95$1, If[LessEqual[y, 4.5e+45], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+221], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000012e-112 or 6.20000000000000013e221 < y

   1. Initial program 88.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 53.8%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -4.50000000000000012e-112 < y < 4.39999999999999983e-247 or 4.4999999999999998e45 < y < 6.20000000000000013e221

   1. Initial program 89.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 33.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if 4.39999999999999983e-247 < y < 4.4999999999999998e45

   1. Initial program 92.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 42.9%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 42.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot a\right)\right)} \]

      2. neg-mul-1 42.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot a\right)\right) \]

   4. Simplified 42.9%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(i \cdot a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-112}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-247}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+221}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 40.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+143} \lor \neg \left(z \leq -5.5 \cdot 10^{+97}\right) \land \left(z \leq -3.1 \cdot 10^{+60} \lor \neg \left(z \leq 3.1 \cdot 10^{+56}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -4.4e+143)
         (and (not (<= z -5.5e+97)) (or (<= z -3.1e+60) (not (<= z 3.1e+56)))))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -4.4e+143) || (!(z <= -5.5e+97) && ((z <= -3.1e+60) || !(z <= 3.1e+56)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-4.4d+143)) .or. (.not. (z <= (-5.5d+97))) .and. (z <= (-3.1d+60)) .or. (.not. (z <= 3.1d+56))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -4.4e+143) || (!(z <= -5.5e+97) && ((z <= -3.1e+60) || !(z <= 3.1e+56)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -4.4e+143) or (not (z <= -5.5e+97) and ((z <= -3.1e+60) or not (z <= 3.1e+56))):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -4.4e+143) || (!(z <= -5.5e+97) && ((z <= -3.1e+60) || !(z <= 3.1e+56))))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -4.4e+143) || (~((z <= -5.5e+97)) && ((z <= -3.1e+60) || ~((z <= 3.1e+56)))))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -4.4e+143], And[N[Not[LessEqual[z, -5.5e+97]], $MachinePrecision], Or[LessEqual[z, -3.1e+60], N[Not[LessEqual[z, 3.1e+56]], $MachinePrecision]]]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000028e143 or -5.50000000000000021e97 < z < -3.1000000000000001e60 or 3.10000000000000005e56 < z

   1. Initial program 89.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 43.8%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -4.40000000000000028e143 < z < -5.50000000000000021e97 or -3.1000000000000001e60 < z < 3.10000000000000005e56

   1. Initial program 90.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 35.2%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+143} \lor \neg \left(z \leq -5.5 \cdot 10^{+97}\right) \land \left(z \leq -3.1 \cdot 10^{+60} \lor \neg \left(z \leq 3.1 \cdot 10^{+56}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 55.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{+37} \lor \neg \left(i \leq 1.55 \cdot 10^{+122}\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -8e+37) (not (<= i 1.55e+122)))
   (* 2.0 (* (* c i) (- a)))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -8e+37) || !(i <= 1.55e+122)) {
		tmp = 2.0 * ((c * i) * -a);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-8d+37)) .or. (.not. (i <= 1.55d+122))) then
        tmp = 2.0d0 * ((c * i) * -a)
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -8e+37) || !(i <= 1.55e+122)) {
		tmp = 2.0 * ((c * i) * -a);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -8e+37) or not (i <= 1.55e+122):
		tmp = 2.0 * ((c * i) * -a)
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -8e+37) || !(i <= 1.55e+122))
		tmp = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -8e+37) || ~((i <= 1.55e+122)))
		tmp = 2.0 * ((c * i) * -a);
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -8e+37], N[Not[LessEqual[i, 1.55e+122]], $MachinePrecision]], N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.99999999999999963e37 or 1.54999999999999999e122 < i

   1. Initial program 92.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 94.3%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 94.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 94.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 94.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 94.3%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 46.7%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto 2 \cdot \color{blue}{\left(-c \cdot \left(i \cdot a\right)\right)} \]

      2. associate-*r* 56.4%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot i\right) \cdot a}\right) \]

      3. distribute-lft-neg-in 56.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-c \cdot i\right) \cdot a\right)} \]

      4. distribute-rgt-neg-in 56.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot \left(-i\right)\right)} \cdot a\right) \]

   8. Simplified 56.4%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot \left(-i\right)\right) \cdot a\right)} \]

   if -7.99999999999999963e37 < i < 1.54999999999999999e122

   1. Initial program 88.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 67.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{+37} \lor \neg \left(i \leq 1.55 \cdot 10^{+122}\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 15: 68.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+82} \lor \neg \left(c \leq 1.05 \cdot 10^{+76}\right):\\ \;\;\;\;i \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.4e+82) (not (<= c 1.05e+76)))
   (* i (* -2.0 (* c (* b c))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.4e+82) || !(c <= 1.05e+76)) {
		tmp = i * (-2.0 * (c * (b * c)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.4d+82)) .or. (.not. (c <= 1.05d+76))) then
        tmp = i * ((-2.0d0) * (c * (b * c)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.4e+82) || !(c <= 1.05e+76)) {
		tmp = i * (-2.0 * (c * (b * c)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.4e+82) or not (c <= 1.05e+76):
		tmp = i * (-2.0 * (c * (b * c)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.4e+82) || !(c <= 1.05e+76))
		tmp = Float64(i * Float64(-2.0 * Float64(c * Float64(b * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.4e+82) || ~((c <= 1.05e+76)))
		tmp = i * (-2.0 * (c * (b * c)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.4e+82], N[Not[LessEqual[c, 1.05e+76]], $MachinePrecision]], N[(i * N[(-2.0 * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.39999999999999998e82 or 1.05000000000000003e76 < c

   1. Initial program 75.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.0%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 68.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 68.8%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 68.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 68.8%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 70.5%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 70.5%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 70.5%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 70.5%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 70.5%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 70.5%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 36.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 36.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 36.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right) \cdot 2}\right)} - 1 \]

      4. distribute-rgt-neg-in 36.8%

         \[\leadsto e^{\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \color{blue}{\left(c \cdot \left(-c\right)\right)}\right)\right) \cdot 2\right)} - 1 \]

   10. Applied egg-rr 36.8%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 36.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2\right)\right)} \]

       2. expm1-log1p 70.5%

          \[\leadsto \color{blue}{\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2} \]

       3. associate-*l* 70.5%

          \[\leadsto \color{blue}{i \cdot \left(\left(b \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} \]

       4. distribute-rgt-neg-out 70.5%

          \[\leadsto i \cdot \left(\left(b \cdot \color{blue}{\left(-c \cdot c\right)}\right) \cdot 2\right) \]

       5. unpow2 70.5%

          \[\leadsto i \cdot \left(\left(b \cdot \left(-\color{blue}{{c}^{2}}\right)\right) \cdot 2\right) \]

       6. distribute-rgt-neg-in 70.5%

          \[\leadsto i \cdot \left(\color{blue}{\left(-b \cdot {c}^{2}\right)} \cdot 2\right) \]

       7. *-commutative 70.5%

          \[\leadsto i \cdot \left(\left(-\color{blue}{{c}^{2} \cdot b}\right) \cdot 2\right) \]

       8. mul-1-neg 70.5%

          \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot \left({c}^{2} \cdot b\right)\right)} \cdot 2\right) \]

       9. *-commutative 70.5%

          \[\leadsto i \cdot \left(\color{blue}{\left(\left({c}^{2} \cdot b\right) \cdot -1\right)} \cdot 2\right) \]

       10. associate-*l* 70.5%

           \[\leadsto i \cdot \color{blue}{\left(\left({c}^{2} \cdot b\right) \cdot \left(-1 \cdot 2\right)\right)} \]

       11. unpow2 70.5%

           \[\leadsto i \cdot \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot b\right) \cdot \left(-1 \cdot 2\right)\right) \]

       12. associate-*l* 71.5%

           \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot \left(c \cdot b\right)\right)} \cdot \left(-1 \cdot 2\right)\right) \]

       13. metadata-eval 71.5%

           \[\leadsto i \cdot \left(\left(c \cdot \left(c \cdot b\right)\right) \cdot \color{blue}{-2}\right) \]

   12. Simplified 71.5%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot \left(c \cdot b\right)\right) \cdot -2\right)} \]

   if -2.39999999999999998e82 < c < 1.05000000000000003e76

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 71.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+82} \lor \neg \left(c \leq 1.05 \cdot 10^{+76}\right):\\ \;\;\;\;i \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 16: 69.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2e+82)
   (* i (* -2.0 (* c (* b c))))
   (if (<= c 2.9e+74)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* (* c i) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2e+82) {
		tmp = i * (-2.0 * (c * (b * c)));
	} else if (c <= 2.9e+74) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2d+82)) then
        tmp = i * ((-2.0d0) * (c * (b * c)))
    else if (c <= 2.9d+74) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * ((c * i) * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2e+82) {
		tmp = i * (-2.0 * (c * (b * c)));
	} else if (c <= 2.9e+74) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2e+82:
		tmp = i * (-2.0 * (c * (b * c)))
	elif c <= 2.9e+74:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * ((c * i) * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2e+82)
		tmp = Float64(i * Float64(-2.0 * Float64(c * Float64(b * c))));
	elseif (c <= 2.9e+74)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * i) * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2e+82)
		tmp = i * (-2.0 * (c * (b * c)));
	elseif (c <= 2.9e+74)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * ((c * i) * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2e+82], N[(i * N[(-2.0 * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e+74], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.9999999999999999e82

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 87.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 87.2%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 74.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 74.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 74.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 74.8%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 74.8%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 41.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 41.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 41.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right) \cdot 2}\right)} - 1 \]

      4. distribute-rgt-neg-in 41.2%

         \[\leadsto e^{\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \color{blue}{\left(c \cdot \left(-c\right)\right)}\right)\right) \cdot 2\right)} - 1 \]

   10. Applied egg-rr 41.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 41.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2\right)\right)} \]

       2. expm1-log1p 74.8%

          \[\leadsto \color{blue}{\left(i \cdot \left(b \cdot \left(c \cdot \left(-c\right)\right)\right)\right) \cdot 2} \]

       3. associate-*l* 74.8%

          \[\leadsto \color{blue}{i \cdot \left(\left(b \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} \]

       4. distribute-rgt-neg-out 74.8%

          \[\leadsto i \cdot \left(\left(b \cdot \color{blue}{\left(-c \cdot c\right)}\right) \cdot 2\right) \]

       5. unpow2 74.8%

          \[\leadsto i \cdot \left(\left(b \cdot \left(-\color{blue}{{c}^{2}}\right)\right) \cdot 2\right) \]

       6. distribute-rgt-neg-in 74.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(-b \cdot {c}^{2}\right)} \cdot 2\right) \]

       7. *-commutative 74.8%

          \[\leadsto i \cdot \left(\left(-\color{blue}{{c}^{2} \cdot b}\right) \cdot 2\right) \]

       8. mul-1-neg 74.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot \left({c}^{2} \cdot b\right)\right)} \cdot 2\right) \]

       9. *-commutative 74.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(\left({c}^{2} \cdot b\right) \cdot -1\right)} \cdot 2\right) \]

       10. associate-*l* 74.8%

           \[\leadsto i \cdot \color{blue}{\left(\left({c}^{2} \cdot b\right) \cdot \left(-1 \cdot 2\right)\right)} \]

       11. unpow2 74.8%

           \[\leadsto i \cdot \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot b\right) \cdot \left(-1 \cdot 2\right)\right) \]

       12. associate-*l* 74.8%

           \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot \left(c \cdot b\right)\right)} \cdot \left(-1 \cdot 2\right)\right) \]

       13. metadata-eval 74.8%

           \[\leadsto i \cdot \left(\left(c \cdot \left(c \cdot b\right)\right) \cdot \color{blue}{-2}\right) \]

   12. Simplified 74.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot \left(c \cdot b\right)\right) \cdot -2\right)} \]

   if -1.9999999999999999e82 < c < 2.9000000000000002e74

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 71.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 2.9000000000000002e74 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 63.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 63.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 63.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 66.1%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 66.1%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 63.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 63.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 68.1%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 68.1%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 68.1%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   12. Step-by-step derivation

       1. expm1-log1p-u 33.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)\right)} \cdot -2 \]

       2. expm1-udef 33.6%

          \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)} - 1\right)} \cdot -2 \]

       3. *-commutative 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{b \cdot \left(\left(c \cdot c\right) \cdot i\right)}\right)} - 1\right) \cdot -2 \]

       4. associate-*l* 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(b \cdot \color{blue}{\left(c \cdot \left(c \cdot i\right)\right)}\right)} - 1\right) \cdot -2 \]

       5. associate-*r* 35.3%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot \left(c \cdot i\right)}\right)} - 1\right) \cdot -2 \]

   13. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} - 1\right)} \cdot -2 \]
   14. Step-by-step derivation

       1. expm1-def 35.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)} \cdot -2 \]

       2. expm1-log1p 71.8%

          \[\leadsto \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \cdot -2 \]

       3. *-commutative 71.8%

          \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)} \cdot -2 \]

       4. *-commutative 71.8%

          \[\leadsto \left(\left(c \cdot i\right) \cdot \color{blue}{\left(c \cdot b\right)}\right) \cdot -2 \]

   15. Simplified 71.8%

       \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)} \cdot -2 \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \]

Alternative 17: 69.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.55e+82)
   (* (* b (* c (* c i))) -2.0)
   (if (<= c 1.22e+75)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* (* c i) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.55e+82) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= 1.22e+75) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2.55d+82)) then
        tmp = (b * (c * (c * i))) * (-2.0d0)
    else if (c <= 1.22d+75) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * ((c * i) * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.55e+82) {
		tmp = (b * (c * (c * i))) * -2.0;
	} else if (c <= 1.22e+75) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * i) * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.55e+82:
		tmp = (b * (c * (c * i))) * -2.0
	elif c <= 1.22e+75:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * ((c * i) * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.55e+82)
		tmp = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0);
	elseif (c <= 1.22e+75)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * i) * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.55e+82)
		tmp = (b * (c * (c * i))) * -2.0;
	elseif (c <= 1.22e+75)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * ((c * i) * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.55e+82], N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[c, 1.22e+75], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.5500000000000001e82

   1. Initial program 81.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 87.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 87.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 87.2%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 74.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 74.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 74.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 74.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 74.8%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 74.8%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 74.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 74.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 76.7%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 76.7%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]

   12. Taylor expanded in c around 0 76.7%

       \[\leadsto \left(\color{blue}{\left({c}^{2} \cdot i\right)} \cdot b\right) \cdot -2 \]
   13. Step-by-step derivation

       1. unpow2 76.7%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

       2. associate-*r* 78.7%

          \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   14. Simplified 78.7%

       \[\leadsto \left(\color{blue}{\left(c \cdot \left(c \cdot i\right)\right)} \cdot b\right) \cdot -2 \]

   if -2.5500000000000001e82 < c < 1.2199999999999999e75

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 71.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 1.2199999999999999e75 < c

   1. Initial program 70.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 88.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 88.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in b around inf 63.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. unpow2 63.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      3. *-commutative 63.2%

         \[\leadsto 2 \cdot \left(-\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      4. associate-*r* 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(\left(c \cdot c\right) \cdot b\right) \cdot i}\right) \]

      5. *-commutative 66.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(b \cdot \left(c \cdot c\right)\right)} \cdot i\right) \]

      6. distribute-lft-neg-out 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-b \cdot \left(c \cdot c\right)\right) \cdot i\right)} \]

      7. *-commutative 66.1%

         \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(-b \cdot \left(c \cdot c\right)\right)\right)} \]

      8. distribute-rgt-neg-in 66.1%

         \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(b \cdot \left(-c \cdot c\right)\right)}\right) \]

   8. Simplified 66.1%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(b \cdot \left(-c \cdot c\right)\right)\right)} \]

   9. Taylor expanded in i around 0 63.2%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 63.2%

          \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

       2. associate-*r* 68.1%

          \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

       3. unpow2 68.1%

          \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   11. Simplified 68.1%

       \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]
   12. Step-by-step derivation

       1. expm1-log1p-u 33.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)\right)} \cdot -2 \]

       2. expm1-udef 33.6%

          \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right)} - 1\right)} \cdot -2 \]

       3. *-commutative 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{b \cdot \left(\left(c \cdot c\right) \cdot i\right)}\right)} - 1\right) \cdot -2 \]

       4. associate-*l* 33.6%

          \[\leadsto \left(e^{\mathsf{log1p}\left(b \cdot \color{blue}{\left(c \cdot \left(c \cdot i\right)\right)}\right)} - 1\right) \cdot -2 \]

       5. associate-*r* 35.3%

          \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot \left(c \cdot i\right)}\right)} - 1\right) \cdot -2 \]

   13. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} - 1\right)} \cdot -2 \]
   14. Step-by-step derivation

       1. expm1-def 35.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)} \cdot -2 \]

       2. expm1-log1p 71.8%

          \[\leadsto \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \cdot -2 \]

       3. *-commutative 71.8%

          \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)} \cdot -2 \]

       4. *-commutative 71.8%

          \[\leadsto \left(\left(c \cdot i\right) \cdot \color{blue}{\left(c \cdot b\right)}\right) \cdot -2 \]

   15. Simplified 71.8%

       \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)} \cdot -2 \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \end{array} \]

Alternative 18: 29.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (z * t)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (z * t)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(z * t))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (z * t);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

2. Taylor expanded in z around inf 25.0%

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

3. Final simplification 25.0%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]

Developer target: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023207 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))